Is there a way to do this?

My hosting for the domain is with GoDaddy, and the A record points to DKPSystem. So, followersofnobility.com will work for our site.

Is there a way to get a mailing list to work with the site, while the A record points here?

I'm aware of the newsletter feature, but it's not quite what I'm looking for.

You would have to find a mailing list host and point the MX records at that particular host. So yes, it's possible to have both your site here, and a mailing list host pointing elsewhere. That's the beauty of using the records directly rather than having users use our DNS servers.

I have a shared hosting plan (multiple servers on one IP address). Can I still configure it to work? What settings would I use?

That one, I'm not sure, to be honest.

If you've got control of your DNS config (as I believe you do, such that you can control the records), you'd just have to find somewhere that handles a mailing list, and you have to set the MX Records to the IP. I don't really know a ton about how mailing lists work, and how the mail configs work, though, so I really don't have much to help you with here. My experience with email configuration is significantly less than my experience with web development.

Sorry I can't be of more help with this one, but it's a bit out of my domain.